Bearing-only containment control of multi-agent systems

Bearing-only containment control means to achieve containment using only the bearing information, rather than the complete relative position information including both the bearing and the distance. Compared with the most existing relative position based containment control algorithms, the bearing-only containment control algorithm is nonlinear due to the nonlinearity of the bearing, which renders the stability analysis challenging. In this article, the bearing-only containment control problem of multi-agent systems with dynamically changing topologies is investigated for two cases, where the leaders are stationary or dynamic. First, when the leaders are stationary, it is shown that the nonlinearity of the bearing leads to the unknown nonlinear time-varying parameters in the system. Based on the boundedness of the nonlinear parameters and the connectivity of the switching directed sensing graphs, it is proven that all the followers converge to the stationary convex hull formed by the leaders asymptotically. Second, when the leaders are dynamic, a distributed estimator is proposed for each follower to keep a local estimate of the velocity of the leaders. Based on the optimality of the projection and the shift invariance of the normal cone, it is proven that all the followers converge to the dynamic convex hull formed by the leaders asymptotically under the conditions on the switching directed sensing and communication graphs. It is shown from the two cases that the distance information is not necessary for containment control, and containment can be achieved as long as the bearing information is provided. Numerical examples are presented to illustrate the theoretical results.